Valeriy and Deque

Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with $$$n$$$ elements. The $$$i$$$-th element is $$$a_i$$$ ($$$i$$$ = $$$1, 2, \ldots, n$$$). He gradually takes the first two leftmost elements from the deque (let's call them $$$A$$$ and $$$B$$$, respectively), and then does the following: if $$$A > B$$$, he writes $$$A$$$ to the beginning and writes $$$B$$$ to the end of the deque, otherwise, he writes to the beginning $$$B$$$, and $$$A$$$ writes to the end of the deque. We call this sequence of actions an operation.

For example, if deque was $$$[2, 3, 4, 5, 1]$$$, on the operation he will write $$$B=3$$$ to the beginning and $$$A=2$$$ to the end, so he will get $$$[3, 4, 5, 1, 2]$$$.

The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him $$$q$$$ queries. Each query consists of the singular number $$$m_j$$$ $$$(j = 1, 2, \ldots, q)$$$. It is required for each query to answer which two elements he will pull out on the $$$m_j$$$-th operation.

Note that the queries are independent and for each query the numbers $$$A$$$ and $$$B$$$ should be printed in the order in which they will be pulled out of the deque.

Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.